Problem: Simplify the following expression: $ q = \dfrac{-9}{8} - \dfrac{-a - 2}{3a} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3a}{3a}$ $ \dfrac{-9}{8} \times \dfrac{3a}{3a} = \dfrac{-27a}{24a} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{-a - 2}{3a} \times \dfrac{8}{8} = \dfrac{-8a - 16}{24a} $ Therefore $ q = \dfrac{-27a}{24a} - \dfrac{-8a - 16}{24a} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-27a - (-8a - 16) }{24a} $ Distribute the negative sign: $q = \dfrac{-27a + 8a + 16}{24a}$ $q = \dfrac{-19a + 16}{24a}$